by George Rhee
Our modern view is that the planets orbit the Sun in elliptical orbits because of the gravitational attraction between them and the Sun. Why did it take hundreds of years to find the correct answer? It took a long time to develop the necessary tools. Tycho’s measuring instruments and the telescope used by Galileo as well as the mathematical tool of the calculus invented by Newton, were the key innovations that made it possible to solve the riddle of planetary motion.
This is a very difficult problem to solve. Imagine you are in the dark on a merry-go-round inside a big tent. On the inside of the tent someone has put lights that twinkle like stars. The merry-go-round is built in a complicated way with arms that can swivel in various directions. Five of your friends are riding on the merry-go-round and they have each been given a small candle to hold in their hands. You then have to deduce from the motion of the candles against the backdrop of stars how the merry-go-round is constructed. This is not an easy task! You have one big advantage over astronomers however. You can feel the air go by when you move, so you know at least that you are in motion. We cannot feel the motion of the Earth, even though modern astronomers believe the Earth is moving at about 200 km per second around the center of our galaxy. Since we feel nothing, it seems natural to assume that we are not moving. The Greeks, as we have mentioned, had considered and rejected the possibility that the Earth does revolve around the Sun.
There is an effect known as parallax, which one would expect to observe due to the Earth’s motion around the Sun. The effect is easily demonstrated. Hold your hand extended at arm’s length in front of you with one finger raised pointing upwards. If you close your right eye and view your finger with your left eye, then close your left eye and view your finger with your right eye, you will notice that your finger will appear to have moved relative to background objects, say at the other end of the room. Now move your finger close to your face, say a foot away, and repeat the experiment. Your finger when held closer to your face will appear to move even more. The object of this exercise is to demonstrate that you can judge the distance of an object (such as your finger) by seeing how much it appears to move when viewed against a distant background (in this case, the back of the room) from two vantage points (your left and right eye). Suppose that at the back of the room there are many stars and that your finger represents a foreground star. Your left eye would represent the position of the Earth in July and right eye the position of the Earth in January. As your finger did in the experiment you just performed, we would expect the foreground star to appear to move relative to the more distant stars when viewed from earth at a 6-month interval.
The Greeks looked for this effect and did not find it, concluding that the Earth is at rest at the center of the universe. This is a great example of the scientific method: You make a hypothesis, which implies a certain outcome for an experiment and perform the experiment. The experimental result does not conform with the prediction and the hypothesis is falsified. This is the method by which the Greeks established that the Earth is at rest. Why didn’t the Greeks observe a parallax?
The parallax is in fact a measurable effect. It was measured for the first time in 1838 by Friedrich Bessel, a German astronomer and mathematician. He measured the parallax of a star called 61 Cygni and determined its distance from the Earth to be 11 light years. This is a huge distance by the way. The Sun is only 8 light minutes away from the Earth. Distances in astronomy are often measured in terms of the distance that light travels in a certain amount of time. A light year, the distance that light travels in a year, is 1016 m. One followed by 16 zeros or about 6 trillion miles.
It thus comes as no surprise that the angular shift that Bessel measured was very small, in fact about one six-thousandth of a moon diameter. The observational accuracy at the time of Hipparchus (c. 190–125 BC) was about one moon diameter. Tycho Brahe (1546–1601) built instruments that improved the accuracy of Hipparchus by a factor of 30; still far short of what was required to detect parallax. It is not possible to make such a measurement without the aid of a telescope. The Greeks had failed to discover parallax because they lacked the technology to measure the positions of stars in the sky to the required accuracy.
When one makes a scientific measurement to determine a small quantity (such as parallax, for instance) and finds nothing, one usually places an upper limit on the result. Instead of saying “the displacement is zero” one says “the displacement is less than some specified value,” which in turn means that the star must be farther away than some specified distance. The same issue arose in the 1980s with the study of neutrino mass. Some scientists thought that since the mass of the neutrino had to be less than a very small number, it was zero. There is now clear evidence that neutrinos have mass. Such dubious lines of reasoning are still present in modern science.
The size of the parallax effect measured by Bessel had important implications. It meant that the distance to the nearest star is much larger than the distance from the earth to the Sun. To put it another way, if we were to shrink the solar system so that the Earth was only nine feet from the Sun, the entire solar system would be the size of a football field and the nearest star would be over 200 miles away. It was hard for Greek scientists to conceive how distant from us the stars really are. To truly mimic the parallax effect with your finger, you would have to hold it 30 or so miles from your face.
The Greek philosopher-scientists were placed on a pedestal and treated as great authorities by scholars working in the Middle Ages. During this period, scientific discussions centered not on nature itself but on Aristotle’s opinion of nature. Science very often progresses thanks to new experiments and improved accuracy in observations. If one turns away from experimental studies and believes that the answers are all to be found by studying books alone, one is on slippery ground. The cult of personality exists in many fields of human endeavor from politics to sports and the arts. To come under the spell of a powerful personality can be great in the development of a person as long as it does not last too long. When this happens to a community of scholars it can stall progress. One can’t question everything all the time but it is good to take some degree of responsibility for the opinions one holds to be true. The key development for astronomy in the middle ages was the construction of precision instruments for measuring angles on the sky and a quantitative understanding of the accuracy of the measurements. With the new measurements made with these new instruments it eventually became clear that all models involving circular orbits were obsolete.
Scientists forge new insights and create new theories because they do not accept the conventional wisdom and because they have access to new tools.
The iconic twentieth century physicists Einstein and Feynman constructed theories using deep physical intuition combined with mastery of mathematical tools. In the field of biology, Francis Crick and James Watson used the new tool of X-ray diffraction to discover the structure of the DNA molecule.
World in Motion
The Greeks had developed an earth-centered model of the universe consisting of nested spheres rotating at uniform speed. This view was to be seriously challenged by a number of scholars in the sixteenth century. Men such as Copernicus, Kepler, Galileo, Tycho, and Newton succeeded in taking what was good about the past and building on it. A mix of tradition and innovation is the key to success in science. As we shall see, these men were working in a very different intellectual climate from that which prevails today. One could be burned at the stake for holding opinions that conflicted with official teachings. In our modern Western world, scientists may be jailed for disseminating military secrets, such as encryption codes, but no one gets persecuted by the government for their astronomical opinions. Climate science may be an unfortunate exception to this rule.
In the Middle Ages we see the development of what is recognizably a university with students working toward degrees in places like Bologna, Paris, and Oxford. Scholars moved from one center of learning to the next, and criticism of the Greek ge
ocentric system began to emerge.
A standard astronomical text of the time was the Tractatus de Sphaera by Johannes de Sacrobosco written around 1230, which gave a simplified description of the standard model of Ptolemy. The totality of the universe was a spherical earth at the center of the solar system with stars placed in a spherical shell beyond Saturn. Nikolaus de Cusa known as Cusanus published in 1404 a book entitled ‘On Learned Ignorance’. Scientists are not searching for the absolute truth but developing ideas or theories that are increasingly closer approximations to the truth. For this process to work one must make repeatable measurements to the best possible accuracy. Cusanus also stated that the Earth was not at the center of the universe and not at rest. He challenged medieval wisdom and set the stage for thinkers such as Giordano Bruno (1548–1600). Bruno believed in the modern idea of an infinite universe with the Sun as just an ordinary star among many.
A Polish monk, Nicolaus Copernicus (1473–1543), studied the Sun-centered system in quite some detail. Copernicus was not employed as a professor when he came up with his original idea concerning a Sun-centered, or heliocentric model of the universe (similarly, Einstein developed some of his theories while working in a patent office in Bern Switzerland). From the Sun-centered or heliocentric theory, a number of points emerged (Fig. 1.1).
Fig. 1.1A comparison of the orbit of Mars in the Earth centered model of Ptolemy (left figure) and the Sun centered model of Copernicus (right figure). In the Copernican system the minimum Mars-Earth distance is AU whereas in the Ptolemaic system it is 1 AU. AU stands for astronomical unit. 1 AU is the average distance between the earth and the Sun, a useful unit of measure for the solar system
First, in the heliocentric model, there is a natural explanation for why Mercury and Venus are never seen very far from the Sun in the sky. This is because in Copernicus’ model they are close to the Sun in space. In the geocentric model this observation has no natural explanation and must be put into the model in an ad hoc manner. Another key point is that retrograde motion emerges as an optical illusion in the Sun-centered model. In the geocentric model the planets must stop in their tracks and reverse path, while in the Sun centered model it only appears that way, as viewed from earth. The planets in the Copernican system all circle the Sun and only appear to move backwards when the earth is overtaking them in their orbits. We can view the solar system as a racetrack, with the inner planets moving faster in space than the outer planets. Once in a while the Earth will catch up with a planet and overtake it and that planet will appear to move backwards in the sky as seen from earth. The Moon, however, really is orbiting the Earth and so never appears to undergo retrograde motion. A strength of the Copernican system is that it accounts for the motions of the planets in a simpler way than the geocentric system. It is, as scientists say, more elegant. Copernicus was not sure whether the universe was infinite or finite, he was aware of the absurdity of the rotation of an infinite universe surrounding the Earth, implying increasing rotation speeds for the more distant stars. It seems in the end that Copernicus placed the stars in a shell beyond Saturn. Thomas Digges (c. 1546–1595) published a version of the Copernican model that includes stars distributed in an unbounded universe.
In practice, the Copernican system was just as cumbersome as the geocentric system in that it required just as many spheres. One reason for this is that, although the planets do in fact circle the Sun, they do not move at uniform speed around the Sun. The Copernican model was also quite inaccurate, being off by as much as ten moon diameters in its prediction of planetary positions in the sky. Setting the Earth in motion raised a number of major problems. If the Earth is in motion, why do we not feel it? When we travel by car, we feel a jolting motion as we accelerate and we feel the bumps in the road. We also have to explain how the Earth goes around the Sun and does not leave the Moon behind.
A formidable but less rational obstacle for the Copernican theory was raised by the fact that the theory contradicted the teachings of the Bible and hence challenged the authority of the church. Copernicus died in 1543 and his book On the Revolution of the Heavenly Spheres was published that same year. Looking back at the sixteenth century from our present-day era, this is striking. These days, scientists rush into press, eager to claim credit for any idea. Copernicus only consented to publication of his theory when he was on his deathbed. Through the publication of his book his name lives forever in the history of science. It is striking that the preface to the first edition contains a disclaimer that would make any lawyer proud. It states essentially that the material in the book is pure and idle speculation and should not be taken literally. The preface implies that anyone who takes the contents of the book seriously is a fool. It turned out that the preface was inserted by a follower of Copernicus who wanted to avoid trouble with church’s authorities. Johannes Kepler, whom we are about to meet, was enraged by this and wrote a critical letter stating that Copernicus did in fact mean what he wrote. The fact that one could come to serious harm for challenging the church’s authority surely explains Copernicus’ hesitation to publish. In the long run, history shows that ideas flourish best in an open society. Attempts to control the flow of knowledge in a totalitarian manner are bound to failure. One can force people to learn nonsense through threats, but one cannot dictate scientific truth from a position of political authority.
Thus far we have described two competing theories of the universe, neither of which is completely satisfying. For further progress on this problem better data were required. The next major actor in our story, Tycho Brahe (1546–1601), provided these data. In terms of modern science, Tycho (traditionally, he is referred to by his first name) strikes me as a politician as well as a researcher. A theorist such as Copernicus needed a pencil, paper, and wastebasket to do his work, as well as a fine mind. To obtain the best set of planetary observations ever made, Tycho needed the sixteenth-century equivalent of a modern research institute, which in turn required funding. He thus needed powers of persuasion to explain to non-scientists who controlled the purse strings why this work was important. It has been suggested that Tycho’s observatory cost a few percent of the income of the King of Denmark. NASA costs a similar fraction of government spending today.
American scientists needed similar skills to Tycho’s when they went to Congress to start lobbying for an optical telescope to be put in space. But let us not carry the analogy too far. Tycho’s institute included dancing bears and dwarves for entertainment but no bears have been spotted at the Space Telescope Science Institute in recent times. Tycho obtained funding from the King of Denmark and set up his research institute on the island of Hveen. He then proceeded to accumulate a database of planetary positions over the next 20 years. Tycho took into account measuring errors, including those due to atmospheric refraction and the flexing of his instruments when they were pointed at different angles in the sky. One of his instruments is shown in Fig. 1.2.
Fig. 1.2One of the sophisticated instruments that Tycho used to make his measurements. This instrument was used to measure the angular position of stars above or below the celestial equator. The large circle has a diameter of 2.7 m. This instrument was completed in 1585 (Published in 1662 and based on Tycho’s original version, this illustration is by Willem Blaeu, a former assistant at Tycho’s Hven observatory. Credit: Collection of Owen Gingerich)
Tycho made an amazing discovery in 1572. He observed the appearance of a new star in the constellation Cassiopeia. We now know that this was an exploding star, or supernova. The star blew itself apart and today over 400 years later we can see an expanding shell of gas where the star once was. The gas is so hot that it glows at X-ray wavelengths. Supernovae play a key role in cosmology, we shall meet them again later in this book. The fact that a star could dramatically change in brightness over a period of mere days was in direct contradiction with Greek cosmology, which stated that the heavens are unchanging. What if the star was not a star but a nearby disturbance? Tycho noted that it sho
wed no parallax, that it seemed fixed in a given constellation. This discovery illustrates a wonderful aspect of science: the unexpected. You set out to do one thing only to find something completely different. In more modern times, radio astronomers set out to study the trails of meteors in the upper atmosphere and discovered very distant galaxies using their radio telescopes.
Tycho constructed a theoretical model that had the planets circling the Sun, which, in turn, circled the Earth. From our present vantage point this model seems contrived, but it was motivated by Tycho’s failure to detect parallax. Eventually, as happens in the best of careers, there was a change of king, and Tycho did not get on with the new king. Tycho eventually left Denmark and ended up in Prague where he was joined by Kepler. It was not until Tycho’s death that Kepler could really get to work analyzing the data. It is for his amazing analysis of Tycho’s data that Johannes Kepler (1571–1630) is known. It resulted in the three laws of planetary motion, for which Kepler is best remembered. The work is a tour de force of mathematical analysis.
The first law states that the shapes of the planets’ orbits are ellipses. An ellipse is like a stretched out circle. An important consequence of this is that the planets are not always at the same distance from the Sun. Kepler’s second law states that planets speed up as they get closer to the Sun in their orbits. The third law states that a planet further from the Sun than the Earth will take longer to orbit the Sun, not only because it has farther to go but because it travels more slowly through space. For example, it takes the planet Jupiter about 12 years to orbit the Sun, but Jupiter only has to cover five times as much distance as the Earth does in its orbit. Should Jupiter’s year not then equal five earth years? The reason it doesn’t is that Jupiter travels around the Sun at a slower speed than the Earth. In many textbooks, ellipses are drawn with a very elongated form. We should bear in mind however, that the orbits of the planets differ from circles at the level of only a few percent. The orbit of mercury, if drawn on this page, would look like a perfect circle to your eyes.
